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Continuation rules matter as much as the die

Part H · L29 · Prerequisite: L28 · One modelling idea

Situation, question, and prediction

Compare an acing d100 that repeats only on 100 with the engine’s Rolemaster-style open-ended helper. The latter opens low on 1–5 and high on 96–100. Predict whether low opening changes to addition when a later 97 appears.

Build

open_ended_d100(max_chain=0) still permits the first extra roll. max_chain caps additional high-result continuations after that. Initial 1–5 chooses subtraction; initial 96–100 chooses addition. Later 96–100 results continue in the same direction. Initial 6–95 stops immediately.

output("Open-ended model, first extra roll only", open_ended_d100(max_chain=0))
output("Open-ended model, one continuation", open_ended_d100(max_chain=1))
output("Above 100 at cap zero", open_ended_d100(max_chain=0).p_ge(101))

Open-ended model, first extra roll only · DieRoll · mean 50.500

outcome	%	frac	X/10000
<-88	0.45	4/889	45
-88..-80	0.45	4/889	45
-79..-71	0.45	4/889	45
-70..-62	0.45	4/889	45
-61..-53	0.45	4/889	45
-52..-44	0.45	4/889	45
-43..-35	0.45	4/889	45
-34..-26	0.45	4/889	45
-25..-17	0.45	4/889	45
-16..-8	0.45	4/889	45
-7..3	0.49	9/1837	49
4	0.01	1/9901	1
6..95	90.0	9/10	9000
97..107	0.45	4/889	45
108..116	0.45	4/889	45
117..125	0.45	4/889	45
126..134	0.45	4/889	45
135..143	0.45	4/889	45
144..152	0.45	4/889	45
153..161	0.45	4/889	45
162..170	0.45	4/889	45
171..179	0.45	4/889	45
180..188	0.45	4/889	45
189	0.05	1/1997	5
>189	0.45	4/889	45

Open-ended model, one continuation · DieRoll · mean 50.500

outcome	%	frac	X/10000
<-88	0.45	4/889	45
-88..-80	0.45	4/889	45
-79..-71	0.45	4/889	45
-70..-62	0.45	4/889	45
-61..-53	0.45	4/889	45
-52..-44	0.45	4/889	45
-43..-35	0.45	4/889	45
-34..-26	0.45	4/889	45
-25..-17	0.45	4/889	45
-16..-8	0.45	4/889	45
-7..3	0.49	9/1837	49
4	0.01	1/9901	1
6..95	90.0	9/10	9000
97..107	0.45	4/889	45
108..116	0.45	4/889	45
117..125	0.45	4/889	45
126..134	0.45	4/889	45
135..143	0.45	4/889	45
144..152	0.45	4/889	45
153..161	0.45	4/889	45
162..170	0.45	4/889	45
171..179	0.45	4/889	45
180..188	0.45	4/889	45
189	0.05	1/1997	5
>189	0.45	4/889	45

Above 100 at cap zero · Prob

outcome	%	frac	X/10000
Above 100 at cap zero	4.90	49/1000	490

Run, read, and check

The high worked path 97,98,4 totals +199. The low path 4,97,3 totals −96: it remains subtraction. At cap zero, above 100 has probability (96+97+98+99+100)/10000 = 0.049. Initial low/high bands balance in the mean, which remains 50.5 for these symmetric caps; tails still differ.

Change one thing

Increase max_chain from zero to one and inspect tails. At zero, minimum is −99 and maximum 200; at one they become −199 and 300. A reported finite maximum is a cap artefact.

Try it yourself

Why is explode(d(100)) not a substitute? Answer: it repeats only the maximum, never subtracts, and has different cap semantics. The chance a continuing chain is truncated here is 0.10 × 0.05^(max_chain+1). Do not call the distribution a particular RMSS printing without a verified source.

Rules and model notes

Implementation-defined mathematical component; RMSS edition/printing source review pending. This teaches the documented helper, not certified Rolemaster attack or manoeuvre rules. No alleged rulebook typo is asserted.

What you now know / where next

Continuation rules matter as much as the die is the reusable idea. Follow the generated previous/next links below, or return to the course index. For a complete self-contained application, see rolemaster-open-ended.

Content ID: L29 · Review status: source pending

Prerequisites: L28